Grating design

ABSTRACT

A method of designing a multi-channel grating structure in a waveguide material, the method comprising the step of utilising a multi-channel grating design function describing an envelope of a refractive index variation defining the multi-channel grating structure in the waveguide material, wherein the multi-channel grating design function deviates from a periodic sampling function multiplied by a single channel grating design function.

FIELD OF THE INVENTION

[0001] The present invention relates broadly to a multi-channel gratingdesign method and to a multi-channel grating structure.

BACKGROUND OF THE INVENTION

[0002] Multi-channel grating structures are typically written intophotosensitive waveguides. The grating structure comprises a refractiveindex variations created in the photosensitive waveguide, which in turndetermine the optical characteristics such as the reflection andtransmission characteristics of the resulting grating structure.

[0003] The envelope of the refractive index variation for amulti-channel grating structure is typically created by applying asampling, i.e. periodic, function to a given single-channel gratingdesign function. The single-channel grating profile is then typically anenvelope of the refrcative index variations achieved by exposing thephotosensitive waveguide through a suitable phasemask or using otherinterferometric techniques.

[0004] In a vast majority of previously reported work on multi-channelgratings, a so-called Sinc-sampled design has been used. For theSinc-sampling approach, an N-channel grating design can be obtained by adirect in-phase summation of N identical seeding gratings [withκ(z)—amplitude grating amplitude, θ(z)—grating phase] equally spaced inthe frequency space: $\begin{matrix}{{{{\sum\limits_{l = 1}^{N}{\kappa \quad ^{\quad\lbrack{{K_{0}z} + \theta + {{({{2\quad l} - N - 1})}\Delta \quad \kappa \quad {z/2}}}\rbrack}}} = {\kappa \quad Q_{{Sin}\quad c}^{\quad {({{K_{0}z} + \theta})}}}},{where}}\begin{matrix}{Q_{{Sin}\quad c} = {\sum\limits_{l = 1}^{N}{\cos \left\lbrack {\left( {{2l} - N - 1} \right)\Delta \quad k\quad {z/2}} \right\rbrack}}} \\{{= {N{\sum\limits_{n = {- \infty}}^{+ \infty}{\sin \quad {c\left\lbrack {{N\left( {{\Delta \quad k\quad z} - {2\quad \pi \quad n}} \right)}/2} \right\rbrack}}}}},}\end{matrix}{{{\sin \quad {c(x)}} \equiv {{\sin (x)}/x}},}} & (1)\end{matrix}$

[0005] and Δk is the channel spacing.

[0006] This design will be referred to as “in-phase” grating designherein after by the applicant.

[0007] An example of this design is shown in FIGS. 4 (c) and (d) withcorresponding spectral characteristics as shown in FIGS. 4 (a) and (b).The maximum value of the refractive index change required to implementthis multi-channel grating design is given by a simple expression:

Δn _(N) ^((max)) =NΔn _(s)  (2)

[0008] where Δn_(s) is the maximum refractive index change required forthe single seeding grating. Since any photosensitive fiber used tofabricate Bragg gratings has material limits of the maximum achievablephotoinduced refractive index change Δn_(N) this represents a limitationon the maximum number of channels that can be recorded in a given fiber.Thus it is highly desirable to reduce a required Δn_(N) as much aspossible. Also it is easy to see that in the chosen example (see FIG. 4)the substantial deviations from the desired (square-like intransmission; linear in group delay) spectral characteristics arepresent. It has been found that such deviations are always present,albeit to different degrees, if a strictly periodic sampling functionapproach is used.

[0009] In another approach, one may solve an inverse scattering problemfor a multi-channel grating directly (i.e. without calculating a singlechannel seeding profile first and then applying a sampling function). Anexample is given in FIGS. 5 (a)-(d). As can be seen, the spectralcharacteristics are substanially perfect, but Δn_(N) is poorlyoptimised.

[0010] At least preferred embodiments of the present invention seek toprovide an alternative multi-channel grating design in which (i) themaximum refractive index change required as a function of the number ofchannels is reduced when compared with the prior art grating designsdiscussed above and (ii) the resulting multi-channel gratings exhibitsubstantially a desired shape, e.g. square-like shape, in theirtransmission co-efficient characteristics.

SUMMARY OF THE INVENTION

[0011] In accordance with a first aspect of the present invention thereis provided a method of designing a multi-channel grating structure in awaveguide material, the method comprising the step of utilising amulti-channel grating design function describing an envelope of arefractive index variation defining the multi-channel grating structurein the waveguide material, wherein the multi-channel grating designfunction deviates from a periodic sampling function multiplied by asingle channel grating design function.

[0012] It has been found that the present invention can provide animproved grating design function when compared with prior art methodsfacilitating design of multi-channel gratings exhibiting a desiredspectral characteristics (e.g. square-like shape in transmission andlinear dependence in group delay).

[0013] In one embodiment, the method comprises calculating the gratingdesign function, and the calculating comprises solving an inversescattering problem for selected multi-channel spectral responsecharacteristics, wherein each partial (single) channel response functiondescribing one channel of the multi-channel spectral responsecharacteristics includes a phase shift value relative to the responsefunctions of the other channels. Preferably, at least one of the phaseshift values is nonzero. In one embodiment, all of the phase shiftvalues are nonzero.

[0014] The method may further comprise the step of determining a set ofthe phase shift values for which an optimisation criterion is met.

[0015] The method may comprise the step of determining a set of thephase shift values for which a maximum of the multi-channel gratingdesign function amplitude is minimised.

[0016] Alternatively, the method may comprise the step of determining aset of the phase shift values for which a maximum difference between aminimum and a maximum of the multi-channel grating design functionamplitude is minimised.

[0017] Alternatively, the method may comprise the step of determining aset of the phase shift values for which a mean-square-deviation in themulti-channel grating design function amplitude is minimised.

[0018] The step of determining the set of phase shift values maycomprise direct scanning through all combinations or conducting avariational analysis, or using other forms of extremum search numericaltechniques, or a simulated annealing—Monte Carlo approach.

[0019] In another embodiment, the method may comprise the step ofdetermining approximate values for the phase shift values.

[0020] The determining of the approximate values may comprise the stepsof forming a summation of periodic functions each describing arefractive index variation along the waveguide, wherein each periodicfunction includes an associated phase shift value relative to the otherperiodic functions, determining a set of associated phase shift valuesfor which an optimisation criteria is met, and using the set ofassociated phase shift values as the approximate values.

[0021] Preferably, the summation. of the periodic functions comprises aFourier analysis. The result of the Fourier analysis may be expressedas: $\begin{matrix}{{\sum\limits_{l = 1}^{N}{\kappa \quad ^{\quad\lbrack{{K_{0}z} + \theta + {{({{2l} - N - 1})}\Delta \quad \kappa \quad {z/2}} + \varphi_{l}}\rbrack}}} = {\kappa \quad Q\quad ^{\quad {({{K_{0}z} + \theta + \psi})}}}} & (3)\end{matrix}$

[0022] In one embodiment, the method comprises the step of determiningthe set of associated phase shift values for which a maximum of theamplitude Q=Q(z) is minimised.

[0023] In another embodiment, the method comprises the step ofdetermining the set of associated phase shift values for which adifference between a maximum and a minimum of the amplitude Q=Q(z) isminimised.

[0024] In another embodiment, the method comprises the step ofdetermining the set of associated phase shift values for which amean-square-deviation in the amplitude Q=Q(z) is minimised.

[0025] The step of determining the set of associated phase shift valuesmay comprise direct scanning through all combinations or conducting avariational analysis, or using other forms of extremum search numericaltechniques, or a simulated annealing—Monte Carlo approach.

[0026] The approximate values may be used as the phase shift values tocalculate the multi-channel grating design function.

[0027] In one embodiment, the method comprises the step of conducting afurther optimisation process using the approximate values as seedingvalues for the phase shift values and using the results of theoptimisation process for calculating the multi-channel grating designfunction.

[0028] The grating may be multi-dimensional, wherein the multi-channelgrating design function is multi-dimensional.

[0029] In accordance with a second aspect of the present invention,there is provided a multi-channel grating structure created utilisingthe design method defined in the first aspect of the present invention.

[0030] In accordance with a third aspect of the present invention thereis provided a multi-channel grating structure, wherein an envelope of arefractive index variation defining the multi-channel grating structuredeviates from a periodic sampling function multiplied by a singlechannel grating design function.

BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Preferred forms of the present invention will now be describedwith reference to the accompanying drawings.

[0032] FIGS. 1 (a)-(d) show claculated spectral charcateristics anddesign of a multi channel grating structure emdbodying the presentinvention.

[0033] FIGS. 2 (a)-(d) show claculated spectral charcateristics anddesign of another multi channel grating structure emdbodying the presentinvention.

[0034] FIGS. 3 (a)-(d) show claculated spectral charcateristics anddesign of another multi channel grating structure emdbodying the presentinvention.

[0035] FIGS. 4 (a)-(d) show claculated spectral charcateristics anddesign of a prior art multi channel grating structure.

[0036] FIGS. 5 (a)-(d) show claculated spectral charcateristics anddesign of a prior art multi channel grating structure.

[0037]FIG. 6 shows an experimental set up for writing a multi-channelgrating structure of a multi-channel grating design embodying thepresent invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0038] The preferred embodiment described provides a multi-channelgrating design which exhibits desired spectral characteristics (e.g.square-like shape in transmission and linear dependence in group delay)and wherein the maximum refractive index change is less than directlyproportional to the number of channels N, thereby improving on prior artmulti-channel grating designs.

[0039] In the preferred embodiment, a multi-channel grating isconstructed by solving the standard inverse scattering problem formulti-channel wavelength-shifted spectral characteristics. This has tobe contrasted with prior art designs, in which a single grating design(seeding grating) is utilised to construct (by appling a samplingfunction) a multi-channel grating.

[0040] Importantly, spectral response functions H_(R)(λ) for partialsingle gratings are being de-phased with respect to each other. In otherwords the inverse scattering problem may be presented as:

H _(R) ^(total)(λ)=H _(R)(λ−λ₁)e ^(iI) ^(₁) +H _(R)(λ−λ₂)e ^(iI) ^(₂) +H_(R)(λ−λ₃)e ^(iI)+ . . .   (4)

[0041] with nonzero relative phases I_(i) in the preferred embodiment.It is to be noted that spectral responses are being de-phased, notpartial seeding gratings themselves. After solving the inversescattering problem for H_(R) ^(total)(λ) the multi-channel gratingdesign function is obtained and may be presented in a form:

q(z)=κQe ^(i(K) ^(₀) ^(z+θ+ψ))  (5)

[0042] where we explicitly retain, for illustrative purposes, the singlechannel grating design function κe^(i(K) ^(₀) ^(z+θ)). The remainingfactors in the expression (5) represent a “sampling” function, which isaperiodic. It is thus not a sampling, i.e. periodic, function anymore,but deviates from a sampling function. This has been found to reducecoupling of light into cladding modes in the resulting grating design.

[0043] It will be appreciated by a person skilled in the art that inorder to optimise the grating design for minimum refractive index changeΔn_(N) as a function of the number of channels N, suitable numerical oranalytical methods can be applied.

[0044] For relatively small number of channels N one can numericallyscan through possible combinations of relative phases I_(i) (solving aninverse scattering problem for each particular combination of dephasingangles I_(i)) and selecting the combination which is optimal accordingto some specific selection criterion (e.g. selecting the combinationwhich minimises maximum required refractive index change).

[0045] For N>>1 location of the optimal set I_(i) is difficult. Evenrough direct scanning through all possible sets of angles (followed byefficient numerical minimum search routines) quickly becomes numericallyinefficient.

[0046] To solve the optimization problem for large N we use, in anexample embodiment, the so-called simulated annealing method—a MonteCarlo approach for minimization of multi-variable functions. Thisstatistical method samples the search space in such a way that there isa high probability of finding an optimal or a near-optimal solution in areasonable time. The term “simulated annealing” is derived from theanalogy to physical process of heating and then slowly cooling asubstance to obtain a crystalline structure. To start, the system stateis initialized. A new configuration is constructed by imposing a randomdisplacement. If the energy of the new state is lower than that of theprevious one, the change is accepted and the system is updated. If theenergy is greater, the new configuration is accepted with someprobability. This procedure allows the system to move consistentlytowards lower energy states, yet still jump out of local minimal due tothe probabilistic acceptance of some upward moves.

[0047] Another approach is to use the approximate equivalence betweenpartial spectra dephasing angles I_(i) and partial grating relativephases φ_(i). Indeed, for weak gratings the first order Bornapproximation holds: $\begin{matrix}{{{{- \frac{1}{2}}{q\left( {z/2} \right)}} = {\int_{- \infty}^{+ \infty}{{r(\beta)}{\exp \left( {{- }\quad \beta \quad z} \right)}{\beta}}}},} & (6)\end{matrix}$

[0048] where q(z) is a grating design function and r(β) is a complexreflection coefficient.

[0049] The Fourier transform (6) is a linear operation with a majorproperty F(a₁r⁽¹⁾+a₂r⁽²⁾)=a₁Fr⁽¹⁾+a₂Fr⁽²⁾. Thus, in this approximation,dephasing of partial gratings is equivalent to dephasing of partialspectral channel responses. Formally the last statement does not holdbeyond weak grating limit. However, in practice, it is stillapproximately correct and the optimal set of angles φ_(i) (for dephasingof partial gratings) may be used as a very good approximation for theoptimal set of partial spectral channel angles I_(i).

[0050] Therefore, the phase shift values I_(i) may be taken from another de-phasing grating design method, which is described in PatentCo-operation Treaty (PCT) patent application no. PCT/AU02/00160 filed on15 Feb. 2002, entitled “Multi Channel Grating Design” assigned to thepresent applicant.

[0051] For example, in partial seeding grating dephasing described inthat applicaition, a sampling function which periodically modulates theamplitude of a given single-channel grating (seeding grating) isutilised, similar to prior art multi-channel grating designs. However,in addition to the periodic modulation of the amplitude of the seedinggrating, different relevant phases φ_(l) for each of thewavelength-seeding gratings are introduced. Accordingly, the resultingdesign function in the preferred embodiment maybe expressed as:$\begin{matrix}{{\sum\limits_{l = 1}^{N}{\kappa \quad ^{\quad\lbrack{{K_{0}z} + \theta + {{({{2l} - N - 1})}\Delta \quad \kappa \quad {z/2}} + \varphi_{l}}\rbrack}}} = {\kappa \quad Q\quad ^{\quad {({{K_{0}z} + \theta + \psi})}}}} & (7)\end{matrix}$

[0052] where the additional phase of the grating ψ=ψ(z) and the samplingamplitude Q=Q(z) are given by. $\begin{matrix}{{{Q^{2}(z)} = {4{\sum\limits_{l,{p = 1}}^{N/2}{{\cos \left( {\alpha_{l} - \alpha_{p}} \right)}{\cos \left( {{n_{l}\Delta \quad k\quad {z/2}} + \beta_{l}} \right)}\cos \left( {{n_{p}\Delta \quad k\quad {z/2}} + \beta_{p}} \right)}}}},} \\{and} \\\begin{matrix}{{{\psi (z)} = {\tan^{- 1}\left\lbrack \frac{\sum\limits_{l = 1}^{N/2}{\sin \quad \alpha_{l}\quad {\cos \left( {{n_{l}\Delta \quad k\quad {z/2}} + \beta_{l}} \right)}}}{\sum\limits_{l = 1}^{N/2}{\cos \quad \alpha_{l}\quad {\cos \left( {{n_{l}\Delta \quad k\quad {z/2}} + \beta_{l}} \right)}}} \right\rbrack}},} & {N\quad {is}\quad {even}}\end{matrix} \\{or} \\{{Q^{2}(z)} = {{4\quad {\sum\limits_{l = 1}^{{({N - 1})}/2}{\cos \quad \alpha_{l}\quad \cos \left( {{n_{l}\Delta \quad k\quad {z/2}} + \beta_{l}} \right)}}} +}} \\{\quad {{{4\quad {\sum\limits_{l,{p = 1}}^{{({N - 1})}/2}{{\cos \left( {\alpha_{l} - \alpha_{p}} \right)}{\cos \left( {{n_{l}\Delta \quad k\quad {z/2}} + \beta_{l}} \right)}{\cos \left( {{n_{p}\Delta \quad k\quad {z/2}} + \beta_{p}} \right)}}}} + 1},}} \\{and} \\\begin{matrix}{{{\psi (z)} = {\tan^{- 1}\left\lbrack \frac{\sum\limits_{l = 1}^{{({N - 1})}/2}{\sin \quad \alpha_{l}\quad {\cos \left( {{n_{l}\Delta \quad k\quad {z/2}} + \beta_{l}} \right)}}}{\sum\limits_{l = 1}^{{({N - 1})}/2}{\cos \quad \alpha_{l}\quad {\cos \left( {{n_{l}\Delta \quad k\quad {z/2}} + \beta_{l} + 1} \right)}}} \right\rbrack}},} & {{N\quad {is}\quad {odd}},}\end{matrix}\end{matrix}$

[0053] where n_(l)≡2l−N−1 and n_(p)≡2p−N−1.

[0054] In the above expressions for Q(z) and ψ(z) we use notationsα≡(φ_(l+φ) _(N+1−l))/2β_(l)≡(φ_(l)−φ_(N+1−l))/2 and set φ_((N+1)/2)=0for odd number of channels. Now for any given N there will be a set of{α_(l)}, {(β_(l)} (or equivalently a set of {φ_(l)} ) which minimizesthe maximum value of Q along the grating structure. By directcalculations it is straightforward to show that $\begin{matrix}{{{\int_{0}^{2\quad {\pi \quad/\Delta}\quad k}{Q^{2}{z}}} = {2\quad \pi \quad {N/\Delta}\quad k}},} & (8)\end{matrix}$

[0055] for any choice of α₁ and β₁. This expression, in turn, leads toan asymptotic formula for the minimum possible Δn_(N) corresponding toan “ideal” situation when Q(z)={square root}{square root over (N)} andonly phase ψ(z) is nontrivially modulated:

Δn _(N) ={square root}{square root over (N)}Δn _(s)  (9)

[0056] We note, that, in practice, the limit Q(z)={square root}{squareroot over (N)} can be reached only approximately.

[0057] Mathematically, one should solve a minimax problem and findQ_(mm)(z;α_(l) ^((opt)),β_(l) ^((opt))) for which max_(z){Q_(mm)(z;α_(l)^((opt)),β_(l) ^((opt)))}=min_((α) _(l) _(,β) _(l) ₎max_(z){Q(z;α_(l),β_(l))}. To find the optimal set φ_(l) for a relatively smallnumber of channels one may use direct numerical scanning through allpossible combinations of the dephasing angles.

[0058] For N>>1 location of the minimizing set (α_(l) ^((opt)), β_(l)^((opt))) is a nontrivial exercise. Again we suggest to use thesimulated annealing method.

[0059] The above described Q_(mm)(z) reduction strategy does not includetrying to avoid touching the zero level at some z. However, zeros in thefibre Bragg grating (FBG) amplitude may lead to the increased phaseerrors (appearance of phase jumps) and should be avoided. Thus,arguably, a better minimization strategy is minimizing its maximumdeviations of Q(z) along z from the theoretical limit level of {squareroot}{square root over (N)}. Mathematically this may be formulated asfinding Q_(dm)(z;α_(l) ^((opt)),β_(l) ^((opt))) for whichmax_(z){Q_(d  m)(z; α_(l)^((opt)), β_(l)^((opt)))} − min_(z){Q_(d  m)(z; α_(l)^((opt)), β_(l)^((opt)))} = min_((α_(l), β_(l)))[max_(z){Q(z; α_(l), β_(l))} − min_(z){Q(z; α_(l), β_(l))}]

[0060] This approach may be implemented by using the same simulatedannealing algorithm described above.

[0061] Another approach will now be described, in which optimization bythe functional minimisation (variational approach) is utilised. The keyproperty of this embodiment is that it relies on estimate of someintegral functional rather than time-consuming numerical scanning in z.Quantitatively, proximity of Q(z) to the theoretical limit {squareroot}{square root over (N)} can be characterised bymean-square-deviation,

ΔQ={square root}{square root over (

(Q(z)−Q)}) ²

  (10)

[0062] where

ƒ(z)

≡{overscore (ƒ)}=Δκ/2π∫₀ ^(2π/Δκ)ƒ(z)dz Ideal optimisation of Q(z)corresponds to the achievement of the average {overscore (Q)}={squareroot}{square root over (N)} and the zero mean-square-deviation from thisaverage value. Using expression (4) and assuming {overscore (Q)}≈{squareroot}{square root over (N)}, one can show that

ΔQ≈{square root}{square root over ((2−E)EN)}  (11)

[0063] where$E = {\frac{1}{4\quad N^{2}}{\sum\limits_{l = 1}^{N}{\sum\limits_{\underset{{{l - p}} \geq 1}{p = 1}}^{N}{\sum\limits_{m = 1}^{N - {{l - p}}}{{\cos \left( {\alpha_{m} - \alpha_{m + {{l - p}}}} \right)}\quad {{\cos \left( {\alpha_{l} + \beta_{l} - \alpha_{p} - \beta_{p} + \beta_{m} - \beta_{m + {{l - p}}}} \right)}.}}}}}}$

[0064] For finding minima of ΔQ the most efficient strategy is again theuse of the simulated annealing method.

[0065] The advantage of the optimisation based on the functionalminimisation compared with direct scanning is the speed: integrationover z is carried out analytically which saves lots of computer time.For odd number of channels variational optimisation leads to a samplingfunction without zeros in amplitude (similar to maximum deviationsminimisation approach). For even number of channels variationaloptimisation leads to a sampling function with zeros in amplitude(similar to maximum minimisation approach).

[0066] The calculated angles (α_(l) ^((opt)),β_(l) ^((opt))) may be useddirectly for partial spectra dephasing of multi-channel grating designsto derive a multi-channel grating design function embodying the presentinvention, which deviates from a periodic sampling function multipliedby a single channel grating design function. In an embodiment of thepresent invention, phase shift values φ_(l), (see equation (7))corresponding to maximum minimisation approach for a four-channelgrating design were determined utilising the above optimisationcalculations, in which α₁=0.5759πn, α₂=0, and β₁=β₂=0 was chosen.

[0067] The phase shift values φ_(l) thus determined were then utilisedas phase shift values I_(i) for the inverse scattering problem as partof this embodiment of the present invention (see equation (4)). Theenvelope of the refractive index variation and transmissioncharacteristics are shown in FIGS. 1(b) and 1(a) respectively. It can beseen that the grating design of the preferred embodiment retains alldesirable spectral characteristics with an almost absolute accuracy. InFIG. 1(d) the envelope of the refractive index variation of FIG. 1(b)has been normalised to the single channel grating design function used,over a limited range, to illustrate the deviation from a periodicsampling function used in prior art designs. The calculated time-delaycharacteristics of this embodiment is shown in FIG. 1(c).

[0068] Another embodiment of the present invention using partial spectradephasing of multi-channel grating design (based on differenceminimisation approach) is shown in FIGS. 2 (a)-(d). The envelope of therefractive index variation and transmission characteristics are shown inFIGS. 2(b) and 2(a) respectively. It can be seen that the grating designof this embodiment also retains all desirable spectral characteristicswith an almost absolute accuracy. In FIG. 2(d) the envelope of therefractive index variation of FIG. 2 (b) has been normalised to thesingle channel grating design function used, over a limited range, toagain illustrate the deviation from a periodic sampling function used inprior art designs. The calculated time-delay characteristics of thisembodiment is shown in FIG. 2(c). All said about the grating designshown in FIG. 1 stays valid, but in addition zeros in gratingapodisation profile are avoided.

[0069] Both of the designs embodying the present invention provide about40% reduction in maximum Δn_(N) in comparison with Sinc-sampling orin-phase inverse scattering-based prior art designs (See FIGS. 4 or 5)and at the same time have substantially ideal characteristics, similarto in-phase inverse scattering-based prior art designs (see FIG. 5).

[0070] It will be appreciated by a person skilled in art that the phaseshift values determined utilising the “partial seeding gratingdephasing” in the embodiments described above may, in other embodiments,be utilised only as an initial set of phase shift values for solving theinverse scattering problem for the multi-channel wavelength shiftedspectral responses. The method of such embodiments then furthercomprises the step of finetuning of dephasing angles using of theinitial set of phase shift values as seeding values. In that way, agrating design is further optimised by further reducing the maximumrefractive index of a given grating design (with seeding dephasingvalues). The standard numerical minimum search techniques (incombination with efficient inverse scattering numerical methods) areutilised for this purpose.

[0071] An example of such a finetuned optimisation embodiment is shownin FIG. 3. The envelope of the refractive index variation andtransmission characteristics are shown in FIGS. 3(b) and 3(a)respectively. It can be seen that the grating design of this embodimentagain retains all desirable spectral characteristics with an almostabsolute accuracy. In FIG. 3(d) the envelope of the refractive indexvariation has been normalised to the single channel grating designfunction used, over a limited range, to illustrate the deviation from aperiodic sampling function used in prior art designs. The calculatedtime-delay characteristics of this embodiment is shown in FIG. 3(c). Onecan see that the maximum refractive index change of this design isslightly (5%) smaller, than the maximum refractive index change of thedesign shown in FIG. 1. Spectral characteristics still remain as good asfor the design of FIG. 1.

[0072] As can be seen from FIGS. 1 to 3, the implementation of themulti-channel grating design of the preferred embodiment in a gratingstructure requires grating writing apparatus with high spatialresolution to be utilised. Therefore, in a grating writing apparatusrelying on photo induced refractive index changes, the apparatuspreferably comprises a beam focusing means to reduce the size of thebeam in the core of the photosensitive waveguide.

[0073]FIG. 6 shows an example experimental set up 50 for writing amulti-channel grating 52 into an optical fibre 54. The experimental setup 50 comprises an interferometer 56 which includes a firstacousto-optic modulation 58 being operated under an acousto-optic waveof a first frequency Ω₁, as indicated by arrow 14. An incoming lightbeam 60 is incident on the first acousto-optic modulator 58 under afirst order Bragg angle. The operating conditions of the acousto-opticmodulator 58 are chosen such that the modulator 58 is under driven,whereby approximately 50% of the incoming beam 60 is diffracted into afirst order beam 62, and 50% passing through the acousto-optic modulator58 as un-diffracted beam 64. The un-diffracted beam 64 is incident on asecond acousto-optic modulator 66 of the interferometer 56 under a firstorder Bragg angle, whereas the beam 62 is not. Accordingly, the beam 62passing through the second acousto-optic modulator 66 without anysignificant loss.

[0074] The second acousto-optic modulator 66 is operated under anacousto-optic wave of a frequency Ω₂, which propagates in a directionopposed the direction of the acousto-optic wave in the first modulator58 as indicated by arrow 68. After the second acousto-optic modulator 66the first order diffracted beam 70 and the beam 62 are frequency shiftedin the same direction (e.g. higher frequency), but by different amountsi.e. Ω₁ v Ω₂.

[0075] The beams 62, 70 are then brought to interference utilising anoptical lens 72, and the resulting interference pattern (at numeral 74)induces refractive index changes in the photosensitive optical fibre 54,whereby a refractive index profile, i.e. grating structure 52, iscreated in the optical fibre 54.

[0076] In FIG. 6, the optical fibre 54 is translated along theinterferometer at a speed ν, as indicated by arrow 74.

[0077] It will be appreciated by a person skilled in the art that theexperimental set up 50 shown in FIG. 6 can be utilised to write amulti-channel grating structure of a multi-channel grating designembodying the present invention through suitable control of the firstand second acousto-optic modulators 58, 66, in conjunction with asuitable control of the speed ν at which the optical fibre 54 istranslated along the interferometer 56 at any particular time. The highspatial resolution required to implement the multi-channel design of thepreferred embodiment is achieved in the set up shown in FIG. 6 byutilising optical lens 72, with the practical limit of the beam size inthe focal plane preferably being of the order of the waveguide coresize.

[0078] It will be appreciated by a person skilled in the art thatnumerous variations and/or modifications may be made to the presentinvention as shown in the specific embodiments without departing fromthe spirit of scope of the invention as broadly described. The presentembodiments are, therefore, to be considered in all respects to beillustrative and not restrictive.

[0079] For example, multi-channel gratings can be created on the basisof the multi-channel grating design of the present invention usingvarious known grating creation techniques, including one or more of thegroup of photo-induced refractive index variation in photo sensitivewaveguide materials, etching techniques including etching techniquesutilising a phasemask, and epitaxial techniques.

[0080] In the claims that follow and in the summary of the invention,except where the context requires otherwise due to express language ornecessary implication the word “comprising” is used in the sense of“including”, i.e. the features specified may be associated with furtherfeatures in various embodiments of the invention.

1. A method of designing a multi-channel grating structure in awaveguide material, the method comprising the step of: utilising amulti-channel grating design function describing an envelope of arefractive index variation defining the multi-channel grating structurein the waveguide material, wherein the multi-channel grating designfunction deviates from a periodic sampling function multiplied by asingle channel grating design function.
 2. A method as claimed in claim1, wherein the method comprises calculating the grating design function,and the calculating comprises: solving an inverse scattering problem forselected multi-channel spectral response characteristics, wherein eachpartial (single) channel response function describing one channel of themulti-channel spectral response characteristics includes a phase shiftvalue relative to the response functions of the other channels.
 3. Amethod as claimed in claim 2, wherein at least one of the phase shiftvalues is nonzero.
 4. A method as claimed in claim 3, wherein all of thephase shift values are nonzero.
 5. A method as claimed in any one ofclaim 2 to 4, wherein the method further comprises the step ofdetermining a set of the phase shift values for which an optimisationcriterion is met.
 6. A method as claimed in claim 5, wherein the methodcomprises the step of determining a set of the phase shift values forwhich a maximum of the multi-channel grating design function amplitudeis minimised.
 7. A method as claimed in claim 5, wherein the methodcomprises the step of determining a set of the phase shift values forwhich a maximum difference between a minimum and a maximum of themulti-channel grating design function amplitude is minimised.
 8. Amethod as claimed in claim 5, wherein the method comprises the step ofdetermining a set of the phase shift values for which amean-square-deviation in the multi-channel grating design functionamplitude is minimised.
 9. A method as claimed in any one of claims 5 to8, wherein the step of determining the set of phase shift valuescomprises direct scanning through all combinations or conducting avariational analysis, or using other forms of extremum search numericaltechniques, or a simulated annealing—Monte Carlo approach.
 10. A methodas claimed in any one of claims 1 to 4, wherein the method comprises thestep of determining approximate values for the phase shift values.
 11. Amethod as claimed in claim 10, wherein the determining of theapproximate values comprises the steps of: forming a summation ofperiodic functions each describing a refractive index variation alongthe waveguide, wherein each periodic function includes an associatedphase shift value relative to the other periodic functions, determininga set of associated phase shift values for which an optimisationcriteria is met, and using the set of associated phase shift values asthe approximate values.
 12. A method as claimed in claim 11, wherein thesummation of the periodic functions comprises a Fourier analysis.
 13. Amethod as claimed in claim 12, wherein the result of the Fourieranalysis is expressed as${\sum\limits_{l = 1}^{N}{\kappa \quad ^{\quad\lbrack{{K_{0}z} + \theta + {{({{2l} - N - 1})}\Delta \quad \kappa \quad {z/2}} + \varphi_{l}}\rbrack}}} = {\kappa \quad Q\quad {^{\quad {({{K_{0}z} + \theta + \psi})}}.}}$


14. A method as claimed in claim 13, wherein the method comprises thestep of determining the set of associated phase shift values for which amaximum of the amplitude Q=Q(z) is minimised.
 15. A method as claimed inclaim 13, wherein the method comprises the step of determining the setof associated phase shift values for which a difference between amaximum and a minimum of the amplitude Q=Q(z) is minimised.
 16. A methodas claimed in claim 13, wherein the method comprises the step ofdetermining the set of associated phase shift values for which amean-square-deviation in the amplitude Q=Q(z) is minimised.
 17. A methodas claimed in any one of claims 13 to 16, wherein the step ofdetermining the set of associated phase shift values comprises directscanning through all combinations or conducting a variational analysis,or using other forms of extremum search numerical techniques, or asimulated annealing—Monte Carlo approach.
 18. A method as claimed in anyone of claims 12 to 17, wherein the approximate values are used as thephase shift values to calculate the multi-channel grating designfunction.
 19. A method as claimed in any one of claims 12 to 17, whereinthe method comprises the step of conducting a further optimisationprocess using the approximate values as seeding values for the phaseshift values and using the results of the optimisation process forcalculating the multi-channel grating design function.
 20. A method asclaimed in any one of the preceding claims, wherein the grating ismulti-dimensional, and wherein the multi-channel grating design functionis multi-dimensional.
 21. A multi-channel grating structure createdutilising the design method as claimed in any one of the precedingclaims.
 22. A multi-channel grating structure, wherein an envelope of arefractive index variation defining the multi-channel grating structuredeviates from a periodic sampling function multiplied by a singlechannel grating design function.